Optical tissue phantoms are necessary for instrument benchmarking and providing a consistent baseline for experiments in various fields of tissue spectroscopy, including diffuse correlation spectroscopy (DCS). To provide the most useful comparisons, a phantom would ideally mimic tissue as closely as possible, including the geometry of static and dynamic scatterers. A branching design that keeps the capillary cross section constant ensures that the same flow velocity is found throughout the phantom while allowing for single input and output fittings to feed all of the capillaries simultaneously. The direction of each capillary is randomized every few millimeters by randomly allocating 2 by 2 "twisting" squares within each layer. These squares swap the locations of four adjacent artificial capillaries either clockwise or counterclockwise. Numerical simulations were used to verify the random walk-like behavior of the capillary paths resulting from this pattern. This is a step toward replicating the randomly varying directionality of actual capillaries. This design was verified by taking DCS measurements at different flow rates of Intralipid through the phantom, demonstrating the effect of the flow rate on the characteristic decay time of the autocorrelation.